
While the dominant is optimal, the lower-order term has cubic dependency (i.e., \(V_\star B_\star ^2\) ) on the scale of the cumulative reward, which is unnatural, and can easily overwhelm the dominant term when \(V_\star B_\star ^2S^3A \gtrsim \sqrt{V_\star B_\star SAK}\) , or \(B_\star \ge (K/(V_\star S^5A))^{1/3}\) . Previous prior-knowledge-free algorithms for SSP [1]}, [2]}, [3]} also suffer from this issue and have at least cubic dependency on the scale of cumulative reward.
